Spectroscopy transition from higher energy level to the

Spectroscopy
is the study of emission, absorption and scattering of radiation when atoms or
molecules undertake transitions between levels differ in energy. It is utilized
to predict and study the molecular structure, different aspects of absorption
and emission, electronic transitions and scattering of light. Electromagnetic
radiations are the swaying electric and magnetic field which are spreading perpendicular
to each other. This oscillation frequency divides the electromagnetic radiation
into different regions for example X-rays, visible, ultraviolet, infrared,
microwaves and radio waves.

In
scattering spectroscopy the energy lost by an incident photon is examined after
it undergoes an interaction with the molecule in which energy is exchanged. In
emission spectroscopy, the analysis of the emitted photon of specie as it
undergoes a transition from higher energy level to the lower energy level is
studied. The analysis of the absorbed photon of incident light as specie
undergoes transition from lower to higher level is studied in absorption
spectroscopy. Quantitative as well as qualitative analysis of a substance can
be done whether the substance is in pure or solution form. From the absorbance
value at any wavelength, we can know the concentration of species of interest
as well as quality of substance from a given wavelength. Decision of occurrence
of specific transition is based on choice rule.

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For
absorption spectrum analysis in ultraviolet (UV) and visible region the general
interest wavelength differ is extremely small. However, it’s of great interest
because the transitions occurring during this vary according to the electronic
transitions in atoms or molecules and it form to the electronic spectrum
analysis. In visible spectrum analysis the interaction of matter and radiations
is established within the sort of color.

Chromophores
give color to the compound. The unsaturated bonds or groups owing to that
substances particularly have color area unit called as radical. Some groups
themselves don’t give color however increase the colors of different
chromophores per area unit termed as auxochromes. For example C=C, C=O, N?N
etc. area unit the models of chromophores. Whereas, C-Br, C-OH, C-NH2 area unit
the models of auxochrome. The presence of chromophores makes the absorption in
200-800nm wavelength vary. The wavelength maxima differ from radical to radical.
An
electron is excited from the lower energy orbital to the higher energy orbital
when a sample is exposed to photon and energy matches the energy of which
required for excitation. The electronic transition would occur from highest
occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital
(LUMO). Wavelength at the absorption is recorded by photometer.

Electronic Transitions

 The absorption of
ultraviolet (UV) or visible radiations are involved with the excitation of
outer electrons of an atom. The electronic transition involves non-bonding n,
sigma ?, pi ? electrons. Typically d and f electrons are also concerned.
Electrons forming single bond are called as the sigma (?) electrons whereas the
electrons forming covalent bond are called as pi (?) electrons. The single or
non-bonding electrons are called as n electrons. Non-bonding electrons are loosely
bound than bonding electrons whereas ? electrons secure a lot of forcefully
than ? electrons. The ?*(anti-bonding orbit) has higher energy than ?* in
excited state.

Transition from bonding to
anti-bonding molecular orbital (N?V)

These
transitions occurring from the bonding orbitals in state to the upper energy
orbitals (anti-bonding orbitals) and called as N?V transitions. These can be
???* or ???* transitions. As an example in parrafins the N?V transitions occur from
???* whereas in olefins these ocuur ???*. The ???* transitions happens in so
much ultraviolet (UV) region whereas ???* transitions are close to ultraviolet
or visible region. ???* transitions occur within the compounds which have double
or triple bonds, aromatic rings, and carbonyl or chemical group. A compound
which have extended conjugation show absorption at higher wavelength. These
transitions typically give molar absorption constant between 1000-10,000
Lmol-1cm-1.

Transitions from Non-bonding to
anti-bonding orbitals (N?Q)

The
transitions occur from nonbonding orbital to anti-bonding are called as N?Q.
These are typically weaker than N?V transition. These may be due to n??* or
n??*. n??* transition mostly happens in the near or far ultraviolet (UV) region
are present in saturated molecules having single bond and unshared electrons
pairs, whereas, n??* transition occurs in the near ultraviolet region or
visible region and are normally present in the compounds where hetero atoms
with unshared electrons are multiply bonded to another atom e.g. C=O, S=O, N=N
etc.

A
chromophore produce two absorption peaks if both lone pair of electrons and pi
electrons are present together. For example in ethanol where oxygen is making
double bond to carbon as well as it has a lone pair of electrons. It means that
there is probability of the n??* transition as well as ???* transition.  Molar absorptivity of n??* transition is less
and is from 10-1000 Lmol-1cm-1 whereas that for ???* transition is high and ranges
from 1000-10,000 Lmol-1cm-1.

Application of UV-Visible
Spectroscopy

The
wide application of UV-Visible Spectroscopy is Beer-Lambert Law. Lambert law
states that the amount of light absorbed is directly related to the path length
and is independent of the intensity of incident light.

Mathematically,

Log
I0/I = ? l

Whereas,
I0 = Intensity of incident light

I=
Intensity of transmitted light

l
= Path length

?
= Extinction coefficient                     

Whereas,
Beer law states that the amount of light absorbed is directly associated with the
concentration of species absorbed or the number of molecules of the species
absorbed within the material.

Log
I0/I   = ? c

Whereas,

I0=
Intensity of incident light

I=
Intensity of transmitted light

?=
Molar Extinction constant

c
= concentration of sample

By
combining both the Beer and Lambert law we get,

Log
I0/I= ?cl

In
the above equation the term log I0 /I is replaced by A, which is
called absorbance

A=
?cl

This
law is the basis of the quantitative analysis of the substance. The system
should obey the Beer-Lambert law for analysis by spectrophotometry.

UV-Visible spectroscopy for
antioxidant activity estimation

Antioxidant
capacity of the compounds can be found out by using ultraviolet spectroscopy.
Antioxidants are can scavenge the free radicals and prevent the oxidation
reaction that can successively break the chain reaction which are a cause of
great damage specially in human body. The preventive power of any drug or
substance shows the quantity of drug required to stop any biological process.
In case of antioxidant activity this amount is signified by IC50. It signifies
the amount of antioxidant substance to reduce the concentration of a certain
radical to 50 percent. Therefore, IC50 is the antioxidant index as well as it signifies
that how much amount of antioxidant is needed to reduce the 50 ? of the
radical. In UV-spectroscopy, the spectra of radical is taken with and without
the addition of antioxidant and then antioxidant activity is determined from
the difference.

The
? radical scavenging activity (RSA) is calculated by using the formula

%RSA=
(AO-A)/AO 100

Where
A0 is the absorbance of radical in the absence of antioxidant and A
is the absorbance presence of antioxidant respectively. Percent radical scavenging
activity rest on the concentration of antioxidant. Graph is plotted between
percent radical scavenging activity (%RSA) and concentration of antioxidant added
and 50% consumption of radical is determined from the straight line and that
concentration of antioxidant is called as IC50. The lower the value of the IC50,
greater is the antioxidant activity.

Scavenging
Constant

The reaction expected
to be taking place in radical scavenging is

For all the molecules
reacting with the radicals the scavenging constant can be evaluated by using
well known Benesi- Hilderbrand equation for free radical scavenging,

A0=
Absorbance of radical in absence of antioxidant

A= Absorbance of
radical in presence of antioxidant

? G= extinction
coefficient of radical in absence of antioxidant

? H-G=extinction
coefficient of radical in presence of antioxidant

C?= amount of
antioxidant added

K= Scavenging constant

Plotting a graph
between AO/A-AO vs. 1/ CO results in straight line and scavenging constant
can be found from the ratio of intercept to slope.

Cyclic Voltammetry

Cyclic
voltammetry is a technique used to acquire qualitative information about
electrochemical reactions. It offers a rapid location of redox potentials of
the electroactive species and measures the connection amongst current and
voltage at the electrode surface when it is plunged in the arrangement of
electroactive species yet the setup is kept unstirred. In this way, the current
estimated is just because of the dispersion of electroactive specie at the surface
of electrode. In cyclic voltammetry the potential is sloped straightly
utilizing triangular waveform. The subsequent plot of current against voltage
is called cyclic voltammogram.

Cyclic voltammogram for a single
electron reversible process

In
cyclic voltammetry of a reversible system, the product of initial oxidation or
reduction is then reduced or oxidized individually on reversing the direction
of the scan.

Linear
sweep cyclic voltammetry depends on the analyte which should be electroactive,
the voltage scanrate and the rate of electron transfer (ET) process. Cyclic
voltammetry highly depends on the analyte being used.

Following
are the basic information which we obtained from cyclic voltammetry:

·       Anodic
and Cathodic peak potentials (Epa, Epc)

·       Peak
potential difference (?Ep)

·       Anodic
and cathodic peak currents (Ipa, Ipc)

·       Formal
or half wave potential (E1/2)

·       Peak
potential at which I= I/2 (Ep/2)

Most
of the time reversible CV wave is displayed by the analyte when all the analyte
is recovered after the scan cycles (forward and reverse). One of the main
criteria of reversible couple is

?EP=
Epa-Epc ?0.058/n

Electron Transfer Process

Electron
transfer is a process which occurs between working electrode and solution
electroactive specie at the electrode surface. It comprises three types which
are as follows

·       Reversible
electron transfer process

·       Irreversible
electron transfer process

·       Quasi-reversible
electron transfer process

Reversible Electron Transfer
Process

in electrochemical reversible process the cell
reverses the reaction by reversing the current and side product will appear or
no new reaction will occur. Following are the characteristics of an electrochemical
reversible electron transfer process.

·       The separation of voltage between the current
peak is

?E = Epa – Epa
= 59/n (mV)

·       The peak voltage position do not change as a
function of voltage scan rate

·       The ratio of the anodic peak current and
cathodic peak current is equal to one

Ipa/Ipa
= 1

·      
The peak
currents are directly related to the square root of the scan rate.

Cyclic voltammogram of reversible electron
transfer

Determination of antioxidant
activity by cyclic voltammetry

Cyclic
voltammetry is an important technique that can be operated for the measurement of
antioxidant activity. Primarily cyclic voltammogram of free radical is recorded
and peak current is noted. Upon successive addition of an antioxidant decrease
in the peak current of free radical is observed which shows quenching of free
radical by an antioxidant and concentration of free radicals get decreased in
this approach.

Following formula used
for determination of percent radical scavenging activity (%RSA) through cyclic
voltammetry.

%RSA
=

 x
100

Where. Ip0 =
Peak current of a free radical

Ip = Peak
current of free radical in the presence of an antioxidant

Plot of (Ip0?Ip)/Ip0
verses different concentration of an antioxidant gives a straight line and from
the value of slope from the graph, antioxidant activity in term of IC30 and
IC50 is obtained.

Calculation
of scavenging constant (ks)

Scavenging constant
(Ks) is typically calculated using Benesi-Hildebrand equation in order to
measure the scavenging strength between the antioxidant and free radical.

                                          Log

 =
logKs + log

      

Whereas,
C? is concentration of an antioxidant added, Ipo is peak current in
the absence of antioxidant, Ip is peak current in the presence of  an
antioxidant, Ks is scavenging constant

 By by means of the
value of scavenging constant, an important thermodynamic parameter i.e. Gibb’s free
energy (?G) can be calculated with the formula given below:

                                                 
?G = ? RT ln Ks                                                                        

Where,
R is gas constant and T is absolute temperature

Calculation of Diffusion
coefficient (D?)

Diffusion coefficient
is a degree of speed with which ion diffuses towards the electrode in a given
solution. It is also known as diffusivity or diffusion constant. It gives you
the extent of the drift of the ions within the solution towards the electrode.
Randle-Sevick equation is used to calculate diffusion coefficient.

iP  = 268, 600 n3/2 AD1/2
C?1/2

iP is the
peak current (µA), n is the number of electrons in Red-ox reaction, F is
Faradays constant (C mol-1), A is an area of an electrode (cm2),
C is the concentration (mol. cm-3), ? is scan rate (V.s-1),
D is diffusion coefficient (cm2.s-1), R is general gas
constant (J K-1 mol-1) and T is the temperature (K).

Basic
Concepts of Theoretical Chemistry

Born
-Oppenheimer Approximation

There are too many variables in the
schrodinger wave equation to be solved for multi- electron system. So many
approximations are proposed and one of the most significant is Born- Oppenheimer
approximation 14. They divide the problem into two parts, in first part the
motion of electron is considered and motion of nuclei is ignored as it is
heavy. The motion of electron is studied in a stationary nucleus charge.

He?e(r,R) =Ee?e(r,R)

He is the electronic Hamiltonian
operator. The Hamiltonian operator becomes now

E=Ee+

All the quantum chemistry methods arises from
this approximation solution. The second problem treats clearly the motion of
the nuclei and reflects electron as an average field. This problem is classical
one not quantum mechanical and it offers to molecular mechanics method.

Basis set

Choice of basis set plays an important role to
increase the accuracy of calculation.

Slater
orbitals function

To solve the schrodinger wave equation, a
mathematical solution to the molecular orbital must be set. In linear
combination of atomic orbitals (LCAO), molecular orbitals ?i necessarily
be written as combination of atomic orbitals ?i.

?i=

Contracted Gaussian function

The slaters type orbitals can also be
contracted into Gaussian type orbitals as a linear function of Gaussian
function,

?m=d1g1+d2g2+d3g3
+……

a normalized Gaussian function for is given
below,

g1s(?,r)=(8?3/?3)1/4e-?r2

Minimal
Basis Sets STO-LG

The original basis set used in Hartee-Fock formulism are STO-LG basis
set, in which each contraction is settled by L primitives (1

). STO-3G is the most
well-known basis set used. This basis set does not produce the
experimental data appropriately and other modifications are needed.

 Double-Dzeta Basis Set

Two contractions are needed in mathematical expression of double-dzeta
basis set rather than one. For example, the 6-31G basis set make use one
contraction to define the inner shell atomic orbitals while the valence atomic
orbitals are defined by two contractions. For the inner shell molecular orbitals,
six primitives form a unique contraction. For the valence atomic orbitals, the earlier
contraction is developed by three primitives and the last by only one
primitive. This mathematical description gives more flexibility in the
description of atomic orbitals. There exists the triple-dzeta basis sets form
from following same idea.

Polarized basis set

Polarization functions are also used to
increase the accuracy. It contains adding p-type contractions on H-atom and
d-type on the heavy atoms

Diffuse
function

The addition of diffusion functions improves
the description far from nuclei. Such basis sets are mentioned as + and ++ for
heavy and hydrogen atoms.  E.g. 6-311++G
(d,p).

Density functional theory

The
Hartree Fock estimate is surely great however it has its confinements. The
confined HF technique can’t depict the separation of atoms into open-shell
fragments. E.g. for phenol the Hartree Fock bond separation vitality is HFBDE =
49.5kcal/mol while the experimental BDE is around 87kcal/mol! The correlation
energy is absent in Hartree Fock guess.

To consider the electronic correlation many
correlated methods have been developed for molecular calculations. Different
post-HF methods have been created, including those based on the Configuration
Interaction approach and multi-reference methods, the Møller-Plesset
perturbation theory (MP2, MP4…), Multi-configurational self-consistent field
approaches (CASSCF, CASPT2…), coupled-cluster methodes. Most of these post-HF
methods permit reaching a very good accuracy, nonetheless the computational
time is dramatically amplified and only relatively small molecular systems can
be considered.

The density functional theory (DFT) considers
the correlation correction and appears as a good stability between the accuracy
and computational cost, letting treating much larger systems than with post-HF.

In DFT the complicated electronic wave functions
are substituted by the electron density, replacing the ?(x1,x2,……)
with ?(r)

?(r1)=N

                             (2.24)

The wave function is extremely mind boggling
and actually this is only a mathematical object, without physical reality. The
fact that is composed as a Slater determinant gives a kind of physical meaning,
as is built with one electron orbitals. Nonetheless, is unquestionably not an interpretable.
It can simply give an interpretable as a reaction to an operator. In that
sense, ?(r) is a very interesting variable since it is directly relates toward
a physical meaning.